# On the size of the maximum of incomplete Kloosterman sums

@article{Bonolis2018OnTS, title={On the size of the maximum of incomplete Kloosterman sums}, author={Dante Bonolis}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={2018} }

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## 2 Citations

### ON THE DISTRIBUTION OF THE MAXIMUM OF CUBIC EXPONENTIAL SUMS

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2018

In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as ‘Birch sums’. Our main theorem gives upper and lower bounds (of…

### The distribution of the maximum of partial sums of Kloosterman sums and other trace functions

- MathematicsCompositio Mathematica
- 2021

In this paper, we investigate the distribution of the maximum of partial sums of families of $m$-periodic complex-valued functions satisfying certain conditions. We obtain precise uniform estimates…

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In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as ‘Birch sums’. Our main theorem gives upper and lower bounds (of…

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We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums $\text{Kl}_{p}(a)$ , as $a$ varies over $\mathbf{F}_{p}^{\times }$ and as $p$ tends to infinity.…

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In 1918 Polya and Vinogradov gave an upper bound for the maximal size of character sums, which still remains the best known general estimate. One of the main results of this paper provides a…

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A classical result of Paley shows that there are infinitely many quadratic characters $\chi\mod{q}$ whose character sums get as large as $\sqrt{q}\log \log q$; this implies that a conditional upper…

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In the analytic study of trace functions of $\ell$-adic sheaves over finite fields, a crucial issue is to control the conductor of sheaves constructed in various ways. We consider cohomological…

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Abstract We show that under certain general conditions, short sums of ℓ-adic trace functions over finite fields follow a normal distribution asymptotically when the origin varies, generalising…

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We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character…

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This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential…